MHB How Can You Test for Symmetry in Mathematics?

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To test for symmetry in mathematics, one can evaluate functions for symmetry about the x-axis, y-axis, and origin. The function y = 2x - 4 is analyzed, revealing it is not symmetric about the y-axis or the origin. When substituting -x into the function, the resulting expression does not match the original, confirming a lack of symmetry. The discussion emphasizes the importance of applying specific rules for testing symmetry in algebraic functions. Overall, understanding these symmetry tests is crucial for analyzing mathematical graphs.
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Test for symmetry about the x-axis, y-axis and origin.

| y | = 2x - 4

What are the rules for testing for symmetry?
 
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RTCNTC said:
Test for symmetry about the x-axis, y-axis and origin.

| y | = 2x - 4

What are the rules for testing for symmetry?

... have you researched "testing graphs for symmetry" ?

Algebra - Symmetry
 
Great! I will answer both symmetry questions tomorrow. Going to work now.
 
| y | = 2x - 4

| -y | = 2x - 4

y = 2x - 4

Symmetric about the x-axis?

| y | = 2(-x) - 4

| y | = -2x - 4

| y | = -2x - 4

Not symmetric about the y-axis.

| y | = 2x - 4

| -y | = 2(-x) - 4

y = -2x - 4

Not symmetric about the origin?
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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